mathwonk
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Posts posted by mathwonk
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Just a question: assuming learning is more effective as a youngster, is it possible it is a better investment to spend big money on young kids, rather than say at Harvard or Stanford as a young adult? I.e. if one would consider spending $40K - $50K/year for tuition on an elite college, is it possible it is better to spend it earlier and then send them to a cheaper college, or hope for a scholarship, after they are already off and running (or up and flying) academically? I.e. what is the best time of life to spend a bundle on instruction? Is it really college? Or is that too late for some purposes?
We spent tuition on private schools at both stages of life, and now looking back, I think it is quite possible my children actually learned more in the earlier period. (Neither went to professional school after college.) Some personal college contacts were valuable, even formative, professionally however. And i could be wrong about how much they learned in college, maybe I just lost touch more with their daily lives.
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There are so many excellent posts here, I don't know if this is worth anything, but since I worked a while on it, I will post.
Even after going through all these stages more than once, it is hard to say something useful on this topic. We always chose what seemed like the best places we could get entrance to, regardless of the cost, but I have wondered since then what it would be like to have back some of those tuition dollars. The problem was always to find a place that could challenge and meet the needs of the child, and offer the opportunities that were realistic for him. If the child seemed to merit a top 5 school, it felt like an adjustment to accept a top 10, or top 30 one, much less top 100.
But even spending lots of money early on did not succeed in placing them where they had to work as hard as they needed to, to develop their talents. Some children differ in this regard, and will work hard in a self directed way, even in a school where intellectual peers are few. But in my own case, and maybe my children’s, the example of a relatively large population of gifted and motivated students was important. It also seems that the intellectual quality of the faculty, along with that of the courses of study, goes up at the upper levels of school rankings. This both benefits and is hard on, a child who glides too easily through prep school and ends up at an elite college.
But everything hinges on the fit, for the child involved. I would ask myself whether the school will challenge this child to his/her capabilities, and offer a future that is within their potential. And will it expose them to the peer and mentor group that will help them realize that potential, including new experiences that have not yet been encountered. In phrasing these criteria, monetary cost actually did not occur to me as a consideration. Part of the reason for this, is that it is my experience that top schools are very wealthy, and are able to genuinely help any child they feel will benefit from and complement their program. But you may need to ask.
Nonetheless, and never having chosen this option, I believe the best monetary bargain, is clearly always available at the state school with a good honors program. This will benefit a child who can flourish within a small subset of peers, at a place with a generally mediocre/average intellectual environment. In my opinion however, even that child may come away from the experience somewhat naive about what is really out there, on their own level. They will be supported, but perhaps not really pushed, at the lower level school. At some point it is useful to find out just how good the people really are with whom you wish to compete and/or collaborate, if that is ones goal.By the way, as a professional mathematician, those honors projects at Auckland look interesting to me.
Also I looked at the list of faculty at Auckland and noticed that Vaughn Jones, Fields medalist, and one of the best mathematicians in the world went there as undergrad. I think that says a lot, i.e. for math preparation a gifted student apparently needs no better place anywhere.
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heres a fairly unbelieveable example of freshman housing, marble bathrooms, etc...: (TS Eliot stayed here.)
http://www.hcs.harvard.edu/~trishin/sergey/galleries/2004/froshdorms/apley/
looks like the thread killer struck again.
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I was in a standard one room double with shared bathroom down the hall. Dorm was built in 1805. No coffee room, no common room, or any other amenities. It was conveniently located near some classroom buildings and libraries. The front door wasn't even locked in those old old days. The only problem that allowed was one night a drunk student wandered in and sucker punched our proctor when ordered to leave.
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I agree with the sentiments in this article of course. I would mention however that competitive math is as much fun for these kids as competitive sports is for children and adults. Thus it helps magnetize them to the subject and give them social validation for what they are good at. My own high school e.g. helped validate us nerds by putting our math trophies in the same display case with the basketball trophies.
Most of the brilliant kids I have taught enjoy these contests and much prefer solving contest problems on their own to being taught canned material, even interesting material. So although competing in contests is a very diferent activity from what they do later as research mathematicians, it seems to be a common part of their experience, and serves to keep them interested until they are ready to branch out on their own.
Rather I think it is learning that needs to be less competitive. Perhaps it is not so much the competitive part of these contests that matters as the challenge. These kids are not challenged in school and they like trying themselves against hard interesting problems. So the distinction I notice between contests and classroom learning is the kid attempts the contest problems on his/her own, instead of just sitting and being spoonfed in class. One can try to adapt clasroom teaching to include this sort of independent behavior, possibly beneficially.
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when our smoke alarm started going off in the house i started cooking virtually all our meals on the charcoal grill outdoors, summer, fall, spring and winter. that was what, 20 years ago? I have a friend who freaks out about carcinogens, but I am healthier than he is. I did get one melanoma but I doubt that was from eating charcoal grilled food. Besides I am over "3 score and 10" so I should be dead anyway. I think I got more carcinogens in the air in Atlanta all those years. In short, I wouldn't worry about it. My friend claimed I wasn't cleaning my grill often enough, so next time i invited him over i bought a brand new grill just for him, and served him from it first time i used it. I suspect being that frightened of your food is worse for your health than charcoal grilled food. Relax and enjoy.
(I do not use starter fluid, but a "chimney" started with paper. I learned this when my neighbor told me he could smell the fumes from the starter fluid. I also tried hard to position the grill so the smoke went down the driveway away from any neighbor's house, but wind is changeable and tricky. Now I live on an isolated 5 acres and no one can smell anything.)
As to the choice between a huge $1200 gas grill and a small manageable $100 charcoal grill that makes food that tastes better, I don't have a big problem there. I do prefer briquettes myself because they all burn completely down to ash, but I also keep hardwood charcoal for my purist friends who like it. The difference is it heats up faster to a hotter temperature, and burns away quicker, and costs more. So you might use it for steaks or something that you want to sear. But for chicken and pork you want a slower fire and briquettes are easier to manage that with.
But i just try to keep everyone happy. The point is to enjoy the experience. I know people who are really skilled grillers, who will only use hardwood charcoal, and even one who brings his own wood in his suitcase when invited, to give the fish or chicken a special flavor. When my son turned 30 I flew in the king of these experts from Boston to Atlanta to give son the best possible grilling experience. We had three grills going and it went off rather well as I recall. When I left Cambridge Mass for Washington state in 1970 I also gave a huge grilling party, for all the hippies in the square, the mathematicians at Brandeis, and the meat luggers I worked with in "Southie". The expert I flew in for my son's bday was one of the principal cooks at that one too. All he needs to put on a majestic occasion is a trench that he digs with a stick, some wood, and a makeshift grill improvised from an old refrigerator shelf. We had a 20-30 foot trench at the big event in 1970.
And now I am reminded it is time to start the grill for the chicken thighs.
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As a grad student I had a quart a day habit in summers. I lived in Canbridge, Mass where there were two competing high quality ice cream vendors: Brigham's and Bailey's almost side by side in the square, so every carton was hand packed. Now we buy the half gallon of Haagen Daz and it lasts a while (still 64 ounces). I got in trouble yesterday when there was none of the 28 ounce "quart" left to go on the blackberry cobbler. We went a long while too with no ice cream, but it has been 90 degrees for 8 days in a row. We picked about 2 gallons of blackberries today too, so we will be hitting it a little harder soon. (We live on a 5 acre lot, where even if you whack back the berries regularly you are still overwhelmed.) I have always owned a hand crank ice cream maker too all my life, and this reminds me I have not used it this year. To me, there is nothing like home made hand cranked "boiled custard" (you don't let it boil) ice cream. My mom refused to eat store bought ever, "if I am going to break my diet it has to be worth it."
Oh and when we buy (or make) ice cream it is always vanilla, anything else is considered adulterated with artificial flavors and often worse stuff, i.e. guar gum, etc... The only ingredients allowed are milk, cream, sugar, eggs, and vanilla. If we want it flavored we add homemade blackberry schnapps, or freshly home made chocolate syrup (just sugar, cocoa, water and maybe a little vanilla, cooked until barely beginning to thicken, but still runny, not gummy like store bought), or in the old days cointreau, before we moved to a state that taxes such luxuries exorbitantly.
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Somehow this struck me as more mean spirited rather than funny, but then I went to Harvard (and the author went to Princeton).
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Here are lectures free online by Ted Shifrin, on honors multivariable calculus, very much in the spirit of an advanced Spivak course. Ted is a superb lecturer and a friend of Mike Spivak, and he consulted on some of the revisions of Spivak's book on one variable calculus. I don't know any source for lectures on the prerequisite one variable honors course.
https://www.youtube.com/playlist?list=PL5I-Eyk8l9FHdJUd9UujGcvumjCFPHbrd
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now its coming back. one of my dormmates had an electric guitar and he said since I was from Nashville, I should sing, so I belted out "Money" by Barrett Strong, and the party went on for much longer than appreciated by the rest of the dorm members.
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If real school were like TIP I would have been much happier to send my kids to school, but it wasn't and they didn't think so either. In fact if it were, there would be no TIP, or at least not at those tuition rates. I wouldn't worry at all, I would just be glad there is such a place where they can get some good instruction and meet new friends.
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interesting discussion. in my opinion the car analogy is insufficient since it assumes everyone can drive all cars. better examples to me would include a stick shift BMW M3 with a 400 HP engine that some drivers would kill themselves in. some tier 1 schools would serve some students about as well as that race car would serve an old man like me. but that's just me being logically picky. and I'm completely out of date on this discussion which has moved way past this and seems to be succeeding excellently. congratulations on this difficult process.
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Here's an off to college story i heard yesterday, and although its biographical facts conflict slightly with what is written on the web about the subject, it was told by one of his close friends and collaborators (Benedict Gross), so may be true. The math prodigy Don Zagier graduated high school at 13 and wanted to go to Oxford, so applied and was accepted until they learned his age, and told him one had to be 16 to go to Oxford. Disappointed he went instead to MIT, graduated at 15, and then went to Oxford as a grad student, since grad school admission there had no age limitation!
All I recall about my own trip to college, taken by train alone at 17, was that when an elderly lady passenger learned I was attending a prestigious ivy league school, she immediately introduced me to her apparently eligible granddaughter.
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It always helps to ask. Anyone who wants you will be as flexible as their situation allows. When I was hired e.g. at a university I was told up front that if I needed more money it was available. I was so clueless I said no, the current offer seemed plenty. Of course after I left grad school and arrived at the university needing housing, schooling etc etc, the offer was much too low, and I was never able to regain the ignored boost even over 40 years. I know you are talking about tuition grants but really it is the same principle: if they want you they will offer something, and you should ask what is available. Just be honest: to me it is not a negotiation in the sense of a game of trying to maximize your profit for bragging rights - it is just saying honestly that you like the school and need so much help to go there. Just remember not to be too modest. In fact you can ask for advice on how much is realistic to live there. I always try dealing honestly and openly with people and they will then usually be as direct and helpful as they can. If not, I would go elsewhere. I never try to play hardball with people I want to be on good terms with. And I concur with those who have observed that an offer may be good only for one year, while after committing there you are stuck for 4 years. And always remember, everything is relative to how much they want you. If you are really a prized catch they will definitely make it possible for you to go there. Do you have any experience in sales? The idea is first to sell the product, then negotiate the price. I.e. once the customer wants the goods, he will pay whatever it costs, as long as he can afford it.
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sahamamama, have you watched the Ingrid Bergman movie: Inn of the 6th happiness?
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Sometimes strong math kids like the pleasure of just sailing through an easier curriculum, and I think that's fine too. My key is to cue it to what they enjoy. But every now and then I throw in something new.
I think I just grasped that you are not actually boring him with the repetitious lessons but testing instead. That's something different.
Have you looked at Euler's book Elements of Algebra? It is free and was written by one of the greatest mathematicians in
history for his butler,who was fairly innocent of math, If your kid can do those problems then no worries.
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I am not a fan of Saxon myself, just the opposite, but I am a big fan of doing whatever works. So if you are getting good results with Saxon, I say go ahead with it. On the other hand if it is boring him and not really challenging him at all, I don't so much. I.e. regardless of my personal opinion based on looking at the materials, I recommend you choose based on how it fits the need you have. I only have the books to go by, while you have both the books and the student's reaction to them to observe. To be honest it sounds as if he doesn't hate them, so why not go ahead. The warning is if he says, "boy this is dull, is all math like this?"
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the cost of living is of course ridiculous in that area, but salaries are also higher, and conceivably the gap between salaries and costs is not that much worse than what the rest of us face wherever we are, i.e. it is always a struggle, but we manage. And the plus side is that there are so many assets available in that area, good weather, good food, good restaurants, good local wine, rich diverse cultures, beautiful spots to visit, great intellectual opportunities (math circles, higher ed,...). Our son moved there in 1991, is still there, and has never regretted it. Good luck and congratulations to your son!
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As a professional mathematician, and former math competition participant, I suggest progressing away from Saxon asap and on to AOPS. The level at which Saxon is pitched is not up to succeeding in math competitions in my opinion. Definitely get some practice taking old tests to avoid a disappointing experience.
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When I was in college the meal plan seemed to be a major money maker for the university and a major source of complaints from the students. Indeed when we finally got permission to live off campus senior year we all put money equal to the meal plan cost into a jar to buy food, and we never needed even a fraction of it to buy MUCH better food than we ever had at school. We joked that we could start a scholarship fund from that jar.
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One piece of advice for kids I have heard, to get an idea of the importance of elite schools, just ask some of the adults you know and admire where they went to college. My dad, for instance, an investigator and agent for the Interstate Commerce Commission safety divison, specializing in train derailments, had only a high school diploma, and was completely self taught in law practice from his reading of "Chitty's Blackstone". Still he argued his own liability cases in federal court for 35 years against the railroad company lawyers, and reportedly never lost a single case. (He had turned down an appointment to West Point to join the railroad at age 16.) My wife, who was chair of her department in the group medical practice she belonged to, graduated from a modest regional college. (She had been recruited to MIT from high school but declined to apply.) In terms of income, I would say both my dad and my wife out - earned me and my Harvard degree, (adjusted for inflation in the first case).
Edit: comment on the cost of education/books: the online copies of Chitty's Blackstone I found today are $500 for a set resembling my dad's, to $20,000 for a rare fine set. When I offered mine for sale last year at a retail store I believe I was offered exactly zero, so gave them away to the library. They then were very probably soon acquired by an antiquarian book seller and offered for sale at going rates. If so, I wish him the best. At least he is keeping them available.
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I'm going to go way out on a limb here and suggest that a 9 year old with his background is already miles ahead in terms of algebra, and suggest just doing maybe little or no math for a while until he wants to do more.
disclaimer: I coerced my 11 year old son to go through about 1/2 of Jacobs' algebra book, and preened when he took first in the state in a math counts contest. Then he rebelled and made his point clearly about his own choices,, so I backed off. He declined in contest performance, but latern majored in math at Stanford and is quite happy today in a high tech job in silicon valley.
the point is that individual choice matters as much or more than acceleration. forgive me for this if it is not what is wanted, but I waited a couple of days and then felt the need to just say it.
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There is something odd about this story to me too. I.e. I cannot understand why anyone would apply to all 8 ivies except for bragging rights. It seems he would have had a better idea of where he wants to go than that. It was more normal in my day to apply to maybe 1 or 2 top schools then a couple middle schools and then an easier admit. It seems likely to me he was recruited in some way to apply to these schools by someone. I'm just thinking there is not really a moral in this story for others since his situation is so unlikely and uncommon. I.e. one should apply to schools that suit your needs rather than ones that will get you onto television. I suspect those schools also do not enjoy being turned down, so I would guess his younger siblings, if they exist, might not get into those schools in the future. But I am very out of touch.
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The University of Georgia in Athens is where I taught for 30 years and in - state tuition there is now about $10,000/year. When we lived in Cambridge MA, for 2 years, my wife took some of her pre med courses at the Harvard extension school evening classes, where one semester classes now cost $1250 each, or also about $10,000 for 8 semester courses. 18 hours of non resident tuition at UW in Seattle is also less than $12,000. They were a lot less 35 years ago, but these prices still sound pretty reasonable to me. This is about half the tuition at one of the cheapest private elementary schools in Atlanta. Of course I spent my whole life devoting most of my income to schools, (honorary Lakota Sioux name: "pays tuition").
A few years ago Georgia also had a lottery funded full tuition scholarship program, the "Hope" scholarship that benefited over 97% of students at the top 3 state schools. It has since reduced benefits since lottery money declined, but provided over $4,000 in tuition for recipients in 2014-2015.
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Proof School?
in Accelerated Learner Board
Posted
i guess I think of choosing schools more in terms of providing stimulation than building a resume. i am probably naive. In my world, i.e. professional mathematics, lasting impressions are made in person, by a` single conversation with a candidate, or even a single remark. I had lunch once with a young man and based on that conversation we hired him years later when he became available. He is now one of the most internationally respected members of our department. I can't even recall looking at his resume but presumably I did. My point is it had no relevance to the decision. In grad school I once brought a brilliant classmate and friend of mine to a class taught by my major professor and my friend asked one question in class. Afterwards the professor told me we needed to give him our department's top fellowship as he was obviously the best student we had. This was the same reaction I had when he had made a single remark during orientation. I recall just turning around and thinking :"who is that?" The student with the best demonstrated ability, which is related to best preparation, is the one who will make this kind of impression.